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In the prequel of this paper, Kauffman and Ogasa introduced new topologicalquantum invariants of compact oriented 3-manifolds with boundary where theboundary is a disjoint union of two identical surfaces. The invariants areconstructed via surgery on manifolds of the form $F \times I$ where $I$ denotesthe unit interval. Since virtual knots and links are represented as links insuch thickened surfaces, we are able also to construct invariants in terms ofvirtual link diagrams (planar diagrams with virtual crossings).  These invariants are new, nontrivial, and calculable examples of quantuminvariants of 3-manifolds with non-vacuous boundary.  Since virtual knots and links are represented by embeddings of circles inthickened surfaces, we refer to embeddings of circles in the 3-sphere as {\itclassical links}. Classical links are the same as virtual links that can berepresented in a thickened 2-sphere and it is a fact that classical links, upto isotopy, embed in the collection of virtual links taken up to isotopy. Wegive a new invariant of classical links in the 3-sphere in the following sense:Consider a link $L$ in $S^3$ of two components. The complement of a tubularneighborhood of $L$ is a manifold whose boundary consists in two copies of atorus. Our invariants apply to this case of bounded manifold and give newinvariants of the given link of two components. Invariants of knots are alsoobtained.  In this paper we calculate the topological quantum invariants of someexamples explicitly. We conclude from our examples that our invariant is newand strong enough to distinguish some classical knots from one another.  We also explain how different Our topological quantum invariants of3-manifolds with boundary and the Reshetikhin-Turaev invariants are. (See thebody for detail).

Quantum Invariants of Links and 3-Manifolds with Boundary defined via Virtual Links: Calculation of some examples